Hybrid signature scheme

ABSTRACT

A signature scheme is provided in which a message is divided in to a first portion which is hidden and is recovered during verification, and a second portion which is visible and is required as input to the verification algorithm. A first signature component is generated by encrypting the first portion alone. An intermediate component is formed by combining the first component and the visible portion and cryptographically hashing them. A second signature component is then formed using the intermediate component and the signature comprises the first and second components with the visible portion. A verification of the signature combines a first component derived only from the hidden portion of the message with the visible portion and produces a hash of the combination. The computed hash is used together with publicly available information to generate a bit string corresponding to the hidden portion.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/421,589 filed on Mar. 15, 2012, which is a continuation of U.S.patent application Ser. No. 12/977,738 filed on Dec. 23, 2010 (now U.S.Pat. No. 8,195,948), which is a continuation of U.S. patent applicationSer. No. 11/812,811 filed on Jun. 21, 2007 (now U.S. Pat. No.7,877,610), which is a continuation of U.S. patent application Ser. No.09/390,362 filed on Sep. 7, 1999 (now U.S. Pat. No. 7,249,259), thecontents of such applications being incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to methods and apparatus for digitallysigning a message.

BACKGROUND OF INVENTION

Digital signatures are used to sign a message generated by acorrespondent so that the origin and authenticity of the message maysubsequently be verified. In its basic form, a digital signature of amessage is generated by signing the message with the originators privatekey. The message may then be recovered using the originators public key.A number of variants of this basic arrangement have been proposed withdifferent attributes. Digital signature schemes are typically thought tofall into two generic classes, namely digital signatures with appendixand digital signatures with message recovery.

Digital signatures with appendix are categorized by the fact that themessage signed is required as input to the verification algorithm.Although very popular (the DSS and ECDSA are examples of this mechanism)they may not provide as much bandwidth efficiency as other methods.

Digital signatures with message recovery are categorized by the factthat the message is not required as input to the verification algorithm.One goal when designing message recovery schemes is to defeatexistential forgery attacks by defining a suitable redundancy functionwhich will distinguish messages legitimately signed from signatures ofrandom bit strings.

In many practical applications the data to be signed carries a certainamount of inherent redundancy. For example, four bytes of data might bereserved for the date but, in practice, 3 bytes suffice and so there are8 bits of redundancy from this field. In order to ensure security it isnecessary to provide a predetermined degree of redundancy within themessage and accordingly the bandwidth efficiency is reduced.

To increase the bandwidth efficiency it is known to split the message into two components, namely a hidden and a visible component. The hiddencomponent is recovered during the verification process and the visibleportion is used as an input to the recovery process. The hiddencomponent must have sufficient redundancy to withstand an existentialforgery attack and additional bits must be added to the message if itdoes not inherently possess this. In one of the proposed standards toimplement such a scheme, ISO 9796 Part 2, the hidden component isutilised to generate a signature component c of the formDES_(R)[H//SHA1(V)//I_(A)] where

H is the hidden component,

V is the visible component

I_(A) is an identifier of the signer

SHA1(V) is a cryptographic hash of the visible component, and

DES_(R) is an encryption of the bit string.

This scheme however has the disadvantage that c is at least the numberof bits in SHAT (V) bits longer, and, as it is included in thesignature, the required bandwidth efficiency may not be achieved.Moreover, the scheme requires invocation of two hash operations as thevalue c is subsequently hashed for inclusion in the signature component.This computational complexity may make it unsuitable for certainapplications.

It is therefore an object of the present invention to provide asignature scheme in which the above disadvantages are obviated ormitigated.

In general terms, one aspect of the present invention provides asignature scheme in which a message is divided in to a first portionwhich is hidden and is recovered during verification, and a secondportion which is visible and is required as input to the verificationalgorithm. A first signature component is generated by encrypting thefirst portion alone. An intermediate component is formed by combiningthe first component and the visible portion and cryptographicallyhashing them. A second signature component is then formed using theintermediate component and the signature comprises the first and secondcomponents with the visible portion.

The generation of the first component from the first portion alonereduces the necessary bandwidth and simplifies the computation. Therelative sizes of the first and second portions are determined by theapplication itself. In this manner, the redundancy function can beapplication dependent as opposed to a global primitive.

Recovery of the message can be completed using the signature and thepublic key of the sender.

According to a further aspect of the invention there is provided averification of a signature of a message that has been subdivided into ahidden and visible portion. The verification combines a first componentderived only from the hidden portion of the message with the visibleportion and produces a hash of the combination. The computed hash isused together with publicly available information to generate a bitstring corresponding to the hidden portion. If the required redundancyis present the signature is accepted and the message reconstructed fromthe recovered bit string and the visible portion.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described by way of exampleonly with reference to the accompanying drawings in which:

FIG. 1 is a schematic representation of a data communication system,

FIG. 2 is a flow chart showing the signature generation,

FIG. 3 is a flow chart showing the verification of the signature of FIG.2, and

FIG. 4 is a flow chart showing a further embodiment of signaturegeneration.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

Referring to FIG. 1, a data communication system includes a pair ofcorrespondents 10, 12 exchanging a message M over a communicationchannel 14. Each of the correspondents 10, 12 includes a cryptographicunit 16, 18 respectively and a terminal 20, 22 to generate and receivethe message M. Each of the cryptographic units 16, 18 implements apublic key encryption scheme that enables it to generate a session key,to encipher or decipher a message using the session key or to sign amessage using a private key whereby the message can then be recoveredusing a public key corresponding to the private key. The generalimplementation of such schemes and their operating principles are wellknown. The encryption scheme may be loaded in to the encryption unitfrom a data carrier coded to implement the protocol under the directionof a general purpose computer or may be implemented on a chipset aspreprogrammed instructions.

In the preferred embodiment described below, the encryption scheme isbased on the intractability of the discrete log problem in finite groupsand is implemented in an algebraic system defined on the points of anelliptic curve over a finite field, typically referred to as ellipticcurve crypto systems. However, the signature scheme proposed may beapplied to any ElGamal signature over any finite group.

The domain parameters of such an elliptic curve crypto system are acurve of the form y²=x³+dx+c and a seed point P. One of thecorrespondents has a private key a, 0<a<n where n is the order of thepoint P and a corresponding public key Q_(A)=aP. The public key may beheld in a certifying authority 24 shown in communication with thecorrespondents 10, 12 by ghosted lines.

The messages M generated by the correspondents 10, 12 are subdividedinto two bit strings H and V (i.e. M=H//V) where H is a bit string whichis hidden and recovered during the verification process and V is a bitstring which is also signed but is required as input to the verificationprocess.

The signature generation algorithm is set out in the flow chart of FIG.2. Initially the bit string H is examined to determine if it containsredundancy above a predetermined limit sufficient to prevent anexistential forgery attack. If the examination determines that theoriginal data forming the message M contains enough redundancy then Hmay simply be a subset of that data. If the predetermined redundancy isnot found then H may be modified to contain artificially addedredundancy such as additional bytes of O's.

By way of example, suppose 80 bits of redundancy is determined to be thepredetermined lower limit for security reasons. If the bit string Hcontains no inherent redundancy then it would be necessary to add up to10 bytes of 0′s. To permit recovery of the message an indicator would beincluded, conveniently as a leading byte in either H or V, which tellsthe number of bytes of 0′s added. Since the value is 0 to 10, 4 bits ofthe byte suffice as an indicator so the bit string contains anadditional 4 bits of redundancy. If t is the number of redundancy bytesthat can be added, then the data must inherently contain at least 80-8 tbits of redundancy.

To sign the message M=H//V the correspondent 10 generates a randominteger k, o<k<n in the cryptographic unit 14. Using k correspondent 10then computes a value of a random point R=kP.

A value c is then computed from the bit string H only such thatc=SKE_(R)(H). SKE_(R) refers to a symmetric-key algorithm under controlof a key derived from the random point R. This could be derived byapplying a function, such as a hash function, to R, truncating R, orusing only one of the coordinates, e.g. the x coordinate as the key. IfH is smaller than the key derived from R, then one possible SKE issimply to XOR H with a truncation of bits from the key derived from R.This effectively is a one-time pad. If H is larger than the key it ispossible to use a DES based algorithm or simply to XOR repeatedly thekey with H.

Using the bit string V, an intermediate component c′ is computed suchthat c′=SHA1 (c//V) where SHA1 is a cryptographically secure hashalgorithm. If preferred, additional information such as a certificate oridentifying information of correspondent 10 may be incorporated in tothe hashed value c′.

It will be noted that the signature component c is the same length asthe hidden portion H as it is a bit wise encryption of that portion andthat the intermediate component c′ is obtained with a single hashoperation.

A signature component s is then computed from the values available tothe correspondent 10 using any of the known ElGamal equations. Aconvenient equation is the Schnorr signature algorithm where s=c′a+k(mod n). A signature is then formed from the components (s,c,V) andforwarded to the correspondent 12.

Verification of the signature by correspondent 12 is performed by theapplication of the corresponding algorithm, as shown in FIG. 3 for theSchnorr signature. The correspondent 12 initially obtains an authenticcopy of the public key Q_(A) of the correspondent 10 from the certifyingauthority 24. The correspondent 12 then computes a value c″=SHA1 (c//V)and derives from the information available in the signature, i.e. s,c,Vand the system domain parameters, the values

X=sP

Y=c″Q_(A)

Z=X−Y

A bit string H′ is then recovered by applying to the received signaturecomponent c the symmetric-key algorithm under control of a key derivedfrom the point Z such that H′=SKE_(z)(c). The bit string H′ is thenexamined to determine if it has the required redundancy and if so thecorrespondent 12 accepts the signature of M and reconstitutes themessage as H′//V.

Because the message M is subdivided, it is only necessary for the oneportion, H, to contain the requisite redundancy. The other portion V,which is sent in the clear, may have the data structure of the originaldata and thereby improve the bandwidth efficiency.

Another feature of this scheme which is of practical and commercialinterest is that the information encoded in c is only available to thoseindividuals who have the public key Q_(A) of correspondent 10. The datacontained in V is available to all. There may be some information whichcorrespondent 10 wants to hide from those not privy to Q_(A) in whichcase the sender, i.e. correspondent 10 puts this information into thebit string H.

For example, in one particular application where the signature is usedto authenticate postage applied to mail, a mailer may not want areceiver to know how many mail pieces he has sent. The post office(which verifies postage and therefore needs this information) has thepublic key of the mailer, and can recover this information onverification but the receiver cannot if he does not have the mailerspublic key.

Of course, if the public key Q_(A) of the sender is contained in theindicium then this is also available to the receiver. Alternatively, thesenders public key may be contained in a certificate that can only berecovered if the receiver has the certifying authority's public key. Ifthis is not generally available then the contents of H will be hiddenfrom the receiver.

As indicated above, alternative forms of signing equations may be used.In a further embodiment shown in the flow chart of FIG. 4, a signingequation similar to the ECDSA standard is used. Normally in such anarrangement:

R=kP

c=DES_(R)(M)r′=SHA1 (c)s=k⁻¹ {SHA1 (c//ID_(A))+a r′} mod n where ID_(A) is an identifier of thesender.the signature is (s,c).When used with a hybrid scheme described above the scheme is modifiedsuch that

R=kP

c=DES_(R)(H)r′=SHA1 (c)s=k⁻¹ {SHA1(c//V)+a r′} modn.the signature is (s, c,V)Again therefore because only a portion H of the message is used togenerate the first component c, only that portion requires a specifiedredundancy. In the balance of the message a reduced redundancy may beutilised to maintain bandwidth efficiency.

The verification for the modified scheme will change accordingly toaccommodate the partial message recovery and necessary redundancy.

We claim:
 1. A method at a correspondent of digitally signing a messagecomprising a recoverable portion and a visible portion, said methodcomprising: encoding said recoverable portion using an encryptionfunction to obtain a first signature component; computing a secondsignature component as a function of said first signature component,said visible portion and a private key associated with saidcorrespondent; and providing a signature comprising said first signaturecomponent, said second signature component and said visible portion assignature components.